Problem: Simplify the following expression: $\dfrac{3z^3}{12z^2}$ You can assume $z \neq 0$.
Solution: $ \dfrac{3z^3}{12z^2} = \dfrac{3}{12} \cdot \dfrac{z^3}{z^2} $ To simplify $\frac{3}{12}$ , find the greatest common factor (GCD) of $3$ and $12$ $3 = 3$ $12 = 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(3, 12) = 3 $ $ \dfrac{3}{12} \cdot \dfrac{z^3}{z^2} = \dfrac{3 \cdot 1}{3 \cdot 4} \cdot \dfrac{z^3}{z^2} $ $\phantom{ \dfrac{3}{12} \cdot \dfrac{3}{2}} = \dfrac{1}{4} \cdot \dfrac{z^3}{z^2} $ $ \dfrac{z^3}{z^2} = \dfrac{z \cdot z \cdot z}{z \cdot z} = z $ $ \dfrac{1}{4} \cdot z = \dfrac{z}{4} $